Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.
Approximate Bayesian inference for latent Gaussian models using inte-grated nested Laplace approximations (with discussion). In order to make spatial statistics computationally feasible, we need to forget about the covariance function Daniel Simpson , Finn Lindgren and Håvard Rue Environmetrics 2012; 23: 65–74Think continuous: Markovian Gaussian models in spatial statistics Daniel Simpson, Finn Lindgren, and Håvard Rue Spatial Statistics 1 (2012) 16–29Although it might happen you have run into one of those cases where INLA is know to fail, it is far more likely it is "the devil is in the details'-effect.You can also use your historical beliefs based on frequency to use the model; it's a very versatile model.For this article, we will be using the rules and assertions of the school of thought that pertains to frequency rather than subjectivity within Bayesian probability. This 'difference' can be using not the same parameters of the prior, using a conditional not a marginal 'initial condition' for the AR(1) model, etc. If there is one tiny difference it will show up in the results, somewhere.